Search results for "Sobolev inequalities"

showing 3 items of 3 documents

In between the inequalities of Sobolev and Hardy

2016

We establish both sufficient and necessary conditions for the validity of the so-called Hardy–Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions. peerReviewed

Mathematics::Functional AnalysisEuclidean spaceHardy-Sobolev inequalities
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Sharp generalized Trudinger inequalities via truncation

2006

Abstract We prove that the generalized Trudinger inequalities into exponential and double exponential Orlicz spaces improve to inequalities on Orlicz–Lorentz spaces provided they are stable under truncation.

Mathematics::Functional AnalysisLorentz spaceTruncationApplied MathematicsMathematical analysisDouble exponential functionMathematics::Classical Analysis and ODEsSobolev inequalitiesOrlicz spacesAnalysisExponential functionSobolev inequalityMathematicsJournal of Mathematical Analysis and Applications
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In between the inequalities of Sobolev and Hardy

2015

We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions.

Pure mathematicsInequalitymedia_common.quotation_subjectDimension (graph theory)Open set35A23 (26D15 46E35)Scale (descriptive set theory)01 natural sciencesSobolev inequalityMathematics - Analysis of PDEsEuclidean spaceClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsmedia_commonComplement (set theory)MathematicsMathematics::Functional AnalysisEuclidean space010102 general mathematicsMathematical analysista111010101 applied mathematicsSobolev spaceMathematics - Classical Analysis and ODEsHardy-Sobolev inequalitiesAnalysisAnalysis of PDEs (math.AP)
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